A valve block includes a fluid-transfer plate with multiple inlet bores connecting to a common inlet channel, and multiple outlet bores connecting to a common outlet channel. The inlet bores and the outlet bores are arranged in a curved shape. The valve block also includes a pressure plate and diaphragm aligned and connected to the fluid-transfer plate in a way that allows pressurized material in the pressure plate to control the state of the channels formed by the inlet and outlet bores.